Find the Equation Using Point-Slope Formula m=4 , (4/3,2)

$m = 4$ , $(\frac{4}{3}, 2)$

Step 1

Use the slope $4$ and a given point $(\frac{4}{3}, 2)$ to substitute for $x_{1}$ and $y_{1}$ in the point-slope form $y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (2) = 4 \cdot (x - (\frac{4}{3}))$

Step 2

Simplify the equation and keep it in point-slope form.

$y - 2 = 4 \cdot (x - \frac{4}{3})$

Step 3

Solve for $y$ .

Simplify $4 \cdot (x - \frac{4}{3})$ .

Rewrite.

$y - 2 = 0 + 0 + 4 \cdot (x - \frac{4}{3})$

Simplify by adding zeros.

$y - 2 = 4 \cdot (x - \frac{4}{3})$

Apply the distributive property.

$y - 2 = 4 x + 4 (- \frac{4}{3})$

Multiply $4 (- \frac{4}{3})$ .

Multiply $- 1$ by $4$ .

$y - 2 = 4 x - 4 (\frac{4}{3})$

Combine $- 4$ and $\frac{4}{3}$ .

$y - 2 = 4 x + \frac{- 4 \cdot 4}{3}$

Multiply $- 4$ by $4$ .

$y - 2 = 4 x + \frac{- 16}{3}$

Move the negative in front of the fraction.

$y - 2 = 4 x - \frac{16}{3}$

Move all terms not containing $y$ to the right side of the equation.

Add $2$ to both sides of the equation.

$y = 4 x - \frac{16}{3} + 2$

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = 4 x - \frac{16}{3} + 2 \cdot \frac{3}{3}$

Combine $2$ and $\frac{3}{3}$ .

$y = 4 x - \frac{16}{3} + \frac{2 \cdot 3}{3}$

Combine the numerators over the common denominator.

$y = 4 x + \frac{- 16 + 2 \cdot 3}{3}$

Simplify the numerator.

Multiply $2$ by $3$ .

$y = 4 x + \frac{- 16 + 6}{3}$

Add $- 16$ and $6$ .

$y = 4 x + \frac{- 10}{3}$

Move the negative in front of the fraction.

$y = 4 x - \frac{10}{3}$

Step 4

List the equation in different forms.

Slope-intercept form:

$y = 4 x - \frac{10}{3}$

Point-slope form:

$y - 2 = 4 \cdot (x - \frac{4}{3})$

Step 5

Find the Equation Using Point-Slope Formula m=4 , (4/3,2)

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